Jack walked up a hill at a speed of x^2 - 11x - 22 miles per hour. Meanwhile, Jill walked a total distance of x^2 - 3x - 54 miles in x - 9 hours. If Jack and Jill walked at the same speed, what is that speed, in miles per hour?
+128475 Jill's speed = distance / time
So equating speeds
x^2 - 11x -22 = (x^2 - 3x - 54) / ( x - 9)
x^2 - 11x - 22 = ( x - 9) ( x + 6) / (x -9)
x^2 -11x - 22 = x + 6 subtract the right side ftom the left and we get that
x^2 - 12x - 28 = 0 factor as
(x - 14) ( x + 2) = 0
Setting both factors to 0 and solving for x produces
x =14 or x = -2
When x = 14 the speed is (14)^2 -11(14) - 22 = 196 - 154 - 22 = 20 mph (pretty fast)
When x = -2 the speed is (-2)^2 - 11(-2) - 22 = 4 + 22 -22 = 4 mph ( this answer is reasonable)
